5 papers
From Block-encoding to Generalized Quantum Signal Processing: Principles, Algorithms and Applications
Tal Gurfinkel, Kaushika De Silva, Anuradha Mahasinghe +9
Modern quantum algorithms are increasingly formulated as coherent procedures for implementing polynomial transformations of operators and singular values. This perspective provides…
Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations
Chon-Fai Kam, Xavier Cadet, Miloud Bessafi +1
Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the netwo…
Quaternionic Response Geometry for Proteins: Toward a Noncommutative Theory of Ordered Deformations
Xiaoting Chen, Chon-Fai Kam, Yu Li +6
Protein function may depend not only on endpoint conformations but also on the ordered deformation histories through which they are reached. This distinction is relevant to alloste…
Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability
Chon-Fai Kam, Xavier Cadet, Miloud Bessafi +1
While world models learn compact representations of complex environments, they lack a physics-grounded metric to assess the structural fidelity of their latent spaces. We identify…
WAN3DNS: Weak Adversarial Networks for Solving 3D Incompressible Navier-Stokes Equations
Wenran Li, Xavier Cadet, Miloud Bessafi +7
The 3D incompressible Navier-Stokes equations model essential fluid phenomena, including turbulence and aerodynamics, but are challenging to solve due to nonlinearity and limited s…